The vapour pressure of a dilute aqueous solution of glucose (C₆H₁₂O₆) is 750 mm of mercury at 373 K. Calculate (i) molality, and (ii) mole fraction of the solution.

The general solutions of $$\,\sin x - 3\sin 2x + \sin 3x = \cos x - 3\cos 2x + \cos 3x$$ is

If $$a,\,b,\,c,$$ are the numbers between 0 and 1 such that the ponts $${z_1} = a + i,{z_2} = 1 + bi$$ and $${z_3} = 0$$ form an equilateral triangle,
then a= .......and b=..........

The equation $${x^{3/4{{\left( {{{\log }_2}\,\,x} \right)}^2} + {{\log }_2}\,\,x - 5/4}} = \sqrt 2 $$ has